More than half of the money lent to Greece so far by the International Monetary Fund and European nations has gone to repay bondholders, a transfer of billions of dollars from taxpayers around the world to European banks and pension funds that invested in the troubled Mediterranean nation.

As the country struggles with a collapsing economy, violent strikes and historic levels of unemployment, a new analysis of an international bailout program shows the degree to which money provided to support Greece has been used to pay off its debts to the private sector.

Under an initial bailout program approved by the IMF and the European Union in May 2010, Greece’s government has been kept afloat by international loans that total $91 billion.

About $52 billion of that has been used to repay bonds that came due between the start of the program and last month, according to a review of the program done for European leaders gathered in Brussels to address financial problems in the 17-nation euro zone.

European banks are among the heaviest investors in Greek bonds. Officials in some developing countries have argued that the IMF, run by a European-dominated board and two consecutive French managing directors, seemed more interested in protecting private investors in Europe than it did when overseeing programs that wiped out dozens of banks during the Asian financial crisis.

The new analysis was presented to European finance ministers, who on Friday approved an $11 billion disbursement to Greece expected in mid-November. The finance ministers, meeting ahead of a gathering of European heads of state Sunday, also worked on programs to bolster the health of the euro region’s banks and boost the effective size of a European bailout fund.

Agreement on a comprehensive plan is considered critical to fix what U.S. officials and others regard as a chief risk to the world economy.

“The crisis in the euro zone is doing real damage to many of the European economies, including Britain,” said George Osborne, Britain’s chancellor of the exchequer. “We have had enough of short-term measures.”

Britain does not use the euro. But, along with the United States, it is concerned about a prolonged downturn or deepening financial crisis in a major world economic zone.

The new data on Greece’s debts illustrate the mammoth burden posed by the country’s more than $300 billion in outstanding loans — an amount that eclipses the size of its economy. It also highlights the risks that IMF and European officials took when they approved the original bailout plan last year without demanding that private investors accept losses on their Greek bonds.

Restructuring a nation’s debt is a well-recognized strategy for cases in which what the country owes outstrips what its taxpayers and companies can repay. The argument at the time, pressed most forcefully by officials from the European Central Bank, was that imposing losses on private investors would wreck the euro region’s credibility and possibly prompt international bond markets to turn on other countries, such as Spain and Italy.

Nearly 18 months later, with billions of dollars in public money already paid out to bondholders, Greece’s situation has only worsened, and Spain and Italy have come under market scrutiny anyway.

The report, prepared by the European Commission in coordination with the central bank and the IMF, found that even under a revised bailout plan approved in July, Greece’s debts were unsustainable. The choices going forward: impose massive losses on private investors, on the order of 50 to 60 percent, or come up with hundreds of billions of dollars in additional lending from the IMF and other public sources.

Talks have been initiated with banks and other private investors about accepting a write-down of their Greek bonds. A cut of 21 percent was included in the July deal, and banks have been reluctant to reopen the issue.

Charles Dallara, managing director of the Institute of International Finance, an industry trade group, said the discussions had made little progress.

“Talks are continuing,” he said, “but we are nowhere near an agreement.”